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- W2030756145 abstract "Let G=(V(G),E(G)) be a simple connected graph and F⊂E(G). An edge set F is an m-restricted edge cut if G−F is disconnected and each component of G−F contains at least m vertices. Let λ(m)(G) be the minimum size of all m-restricted edge cuts and ξm(G)=min{|ω(U)|:|U|=m and G[U] is connected}, where ω(U) is the set of edges with exactly one end vertex in U and G[U] is the subgraph of G induced by U. A graph G is optimal-λ(m) if λ(m)(G)=ξm(G). An optimal-λ(m) graph is called super m-restricted edge-connected if every minimum m-restricted edge cut is ω(U) for some vertex set U with |U|=m and G[U] being connected. In this note, we give a characterization of super 2-restricted edge-connected vertex transitive graphs and obtain a sharp sufficient condition for an optimal-λ(3) vertex transitive graph to be super 3-restricted edge-connected. In particular, a complete characterization for an optimal-λ(2) minimal Cayley graph to be super 2-restricted edge-connected is obtained." @default.
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- W2030756145 date "2011-12-01" @default.
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- W2030756145 title "On super 2-restricted and 3-restricted edge-connected vertex transitive graphs" @default.
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- W2030756145 doi "https://doi.org/10.1016/j.disc.2011.08.021" @default.
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